MATH 107
PRACTICE TEST 2-Chap. 8(Sec.A, B), Chap. 9(Sec. B, C)
1. Decide whether the following statement makes sense or doesn’t make sense. Explain your reasoning.
a. A toxic chemical decays with a half-life of 10 years, so half of it will be gone 10 years
from now and all the rest will be gone 20 years from now.
b. The graph of a linear function is sloping downward (from left to right) so the rate of
change is negative.
2. The population of Deer Park is increasing by 108 people per year. State whether this growth is linear or exponential.
If the population is 3652 today, what will the population be in 4 years?
3. At the beginning of a period of hyperinflation in Zimbabwe, the food bill for a small family was
$9 a month increasing at a rate of 84% per month.
a) Create a table for the cost of the food bill for at least the first five months of hyperinflation .
b) What was the cost of the food bill for a small family after 5 months of hyperinflation?
c) Graph the values in your table labeling your axes appropriately.
d) Does the graph illustrate exponential or linear growth?
4. A $665 washing machine at Squeaky’s Laundromat can be depreciated for tax purposes at a rate of $95 per year.
a) Find a linear function for the depreciated value of the washing machine as it varies with time.
b) When does the depreciated value reach 0?
5. If the population of Cheney increases by 60 people each year, when will the current population of 10,590 double
(round to the nearest year)?
6. Poaching caused the population of African elephants to decline by 8% per year beginning in 1979. In what year, was
the population reduced to half(half-life of population)? In 1979, there were 1.3 million elephants, how many remained
in 1990?
7. Researchers are studying the H1N1 virus in the laboratory and have determined the virus grows at a rate of 8% per
hour. What is the approximated doubling time for the H1N1 virus?
8. The price of a computer component is decreasing at a rate of 15% per year. State whether this decrease is linear or
exponential. If the component cost $110 today, what will it cost in 3 years?
9. You can rent a car at Cheap Cars for $12 per day plus an additional 15¢ per mile. Jack is given a travel allowance by
his company of $45 per day for a rental car. How many miles can Jack drive each day and not go over budget?
10. The drug Valium is eliminated from the blood stream exponentially with a half-life of 36 hours. Suppose that a patient
receives an initial dose of 80 mg of Valium at midnight.
a) How much Valium is in the patient’s blood at noon on the first day?
b) Estimate when the Valium concentration will reach 30% of its initial level.
11. The county assessor claims the value of your house is increasing by $2400 per year. If it is worth $160,000 today,
what will it be worth in 5 years?
12. Assuming flies grow exponentially, the doubling time of a population of flies is 6 hours. By what factor does the
population increase in 1 week?
13. The initial population of a town is 3300 and every 10 years the population doubles. What will the population be in
10 months? 12 years?
14. A leprechaun places a magic penny under a girl’s pillow. The next night there are 2 magic pennies under her pillow.
The girl now has 3 magic pennies. Each night the number of magic pennies under her pillow is double the number
she received the previous night. How many magic pennies will the girl have collected after 10 nights?
15. The average price of a home in Spokane Valley was $172,000 in July,2008, but a local realtor states that home prices
have been falling since 2008 at a rate of 4% per year.
a) Find an exponential function of the form, 𝑄 = 𝑄0 ∙ (1 + 𝑟)𝑡 , to model the situation described above.
b) Based on the model, what would you expect to be the average price of a home in Spokane Valley in 2014?
16. An economic indicator is increasing at the rate of 6% per year. What is its doubling time? By what factor will the
indicator increase in 5 years?
17. The half-life of an anti-depressant drug in the bloodstream is 18 hours. What fraction of the original drug dose
remains in a person’s bloodstream after 24 hours? 60 hours?
18. You drive along the highway at a constant speed of 65 miles per hour.
a) How far do you travel in 4.7 hours?
b) If you plan to travel to Portland 351 miles away, assuming a constant speed of 65 mph, how long will it take
to reach Portland?
19. The average price of a home in Spokane Valley was $172,000 in July 2008 and decreased to an average price of
$144,000 in July 2012. Assuming the decrease was linear, what is the rate of change in the average price of a home
in Spokane Valley(include units)?
20. The approximate doubling time for an investment is 12 years. What is the growth rate per year?
21. In the bacteria in a bottle parable, one bacteria starting dividing at 11:00 am and continued to double in amount every
minute until the bottle became full at noon.
a) How many bacteria are in the bottle at 11:20 am?
b) At what time was the bottle 1/8 full?
22. Andrew’s speedometer on his moped quit working so he recorded the number of miles traveled and the time to travel
that distance and plotted that information on the graph below:
a) Determine the rate of change in miles per minute from the graph he created below.
b) How fast did his moped travel in miles per hour?
23. Consider the following graph where p corresponds to profit in dollars and s corresponds to number of smoothies sold
below:
a) Write a statement which describes how one variable varies with respect to the other variable in the situation
depicted in the graph.
b) Find the rate of change(include units).
c) Briefly discuss the conditions under which a linear function is a
realistic model for the given situation.
24. A fundraiser offers raffle tickets for $5 each. The prize for the raffle is a
$400 jewelry set, which must be purchased with proceeds from the ticket
sales. Find a function that gives the profit/loss for the raffle as it varies
with the number of tickets sold. How many tickets must be sold for the
raffle sales to equal the cost of the prize?
25. Some climbers begin climbing at an elevation of 5300 feet and ascend at
a steady rate of 500 vertical feet per hour.
a) Define the independent and dependent variables.
b) Draw a graph of the situation labeling your axes with the variables
and units used.
c) Estimate the climbers elevation after 3.5 hours using the graph.
Math 107 Practice Test 2 Chap. 8 and 9 ANSWERS
1a. Doesn’t make sense. In 20 years, a quarter of the amount of toxic chemicals will be left. It will not be all
gone.
b. Does make sense. If the linear functions is sloping downward the value is decreasing which has a negative
rate of change.
2. linear; 4084 people
3a.
b. $189.82
Months
Cost($)
0
9
1
16.56
2
30.47
3
56.07
4
103.16
5
189.82
c. A curve beginning at (0,9) and curving upward with Cost ($) on the vertical axis and months on the hor. Axis.
d. Exponential
4a. 𝑉 = 665 − 95𝑡 where V=depreciated value of washing machine and t=years since purchase
b. 7 years
5. 177 years
6. 1988; 519,528
7. 8.75 hrs
8. exponential; $67.55
9. 220 miles
10a. 63.5 mg
b. aprrox. 63 hours
11. $172,000
12. 228 = 268,435,456
13. 3496; 7581
14. 1023
15a. 𝑄 = 172,000(0.96)𝑡 where t=years since 2008 and Q=average price of home
b. $134,634.34
16. 11.90 yrs; 1.34
17. 0.397; .099
18. 305 mi.; 5.4 hrs.
19. -$7000/yr
20. 5.83%
21a. 220 = 1,048,576
b. 11:57 am
22a. 0.4 mile/min
b. 24 mph
23a. Profit in dollars varies with respect to number of smoothies sold.
b. $3 profit/smoothie sold
c. When you increase smoothies sold to a large number you may need to increase the number of workers
needed which will change your profit per smoothie. Also, you can’t sell a negative amount of smoothies.
24. 𝑃 = 5𝑡 − 400 where P=profit from raffle($) and t=number of tickets sold; 80 tickets
25a. Ind. Var.= hours climbed, dep. Var.=elevation in feet
b. Straight line starting at 0 hours and 5300 ft increasing left to right at 500 ft/hr
c. 7050 feet